Day on Exclusion Processes
AugsburgMünchen
Friday, 17 Dec 2021
Speakers: Ofer Busani (Bonn), Peter Nejjar (Bonn) and Dominik Schmid (Princeton)
Schedule and speakers 

14:1515:15  Dominik Schmid: Mixing times for the TASEP 
15:1516:15  Peter Nejjar: Mixing and KPZ fluctuations of ASEP 
Tea  
16:4517:45  Ofer Busani:
Diffusive scaling limit for the Busemann process in last passage percolation 
The talks are in lecture hall B 004 (ground floor)
Hybrid meeting: participation possible live (`2G rule' applies) or online via zoom; zoom link provided at this website in due time.
Abstracts:
Ofer Busani: Diffusive scaling limit for the Busemann process in last passage percolation
In last passage percolation, i.i.d. weights are assigned to the vertices of the lattice Z^2 and one is interested in the behavior of geodesics  upright paths on the lattice that maximize the weight collected between their endpoints. Of particular interests is the behavior of infinite geodesics  infinite upright paths such that any connected subset of them is a geodesic. One of the most useful tools in studying infinite geodesics is the Busemann process, a stochastic process that holds much information on the behavior of infinite geodesics. In this talk I will describe the scaling limit of the Busemann process in exponential last passage percolation, the motivation behind it, and discuss some new ideas and connections from the proof.
Peter Nejjar: Mixing and KPZ fluctuations of ASEP
The fluctuation behavior of the asymmetric simple exclusion process (ASEP) on the integers is governed by a 1/3 fluctuation exponent and TracyWidom limit laws. In this talk, we will show how this fluctuation behavior translates into the mixing behavior of the ASEP on the segment and gives the cutoff window and profile. The key tool for this translation are hitting times. To understand these hitting times, we use an algebraic symmetry visible on the level of the multispecies ASEP. This is joint work with Alexey Bufetov (Leipzig).
Dominik Schmid: Mixing times for the TASEP
The exclusion process is one of the beststudied examples of an interacting particle system. In this talk, we focus on simple exclusion processes on finite graphs. We give an overview over some recent results on the mixing time of the (totally) asymmetric simple exclusion process in one dimension, using coupling arguments and a connection to last passage percolation. This talk is based on joint work with Nina Gantert and Evita Nestoridi.
Organizers: Nina Gantert(TUM), Stefan Grosskinsky (Augsburg), Markus Heydenreich (LMU), Bernd Schmidt (Augsburg),